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Basic Sets of a Diffraction Pattern. S. Ciccariello^a and A. Cervellino^b, ^aDip.to di Fisica “G.Galilei” and INFM, I-35131 Padova, Italy, ^bETH - Laboratory of Crystallography, CH-8092 Zurich, Switzerland.

The full diffraction pattern of a crystal with point-like atoms can be recursively reconstructed from the intensities relevant to an appropriate finite subset of reflections, named basic set of reflections [1]. The procedures able to single out such basic sets, in particular the one yielding the smallest basic set, are reported. The recursive procedure also allows us to determine the polynomial equations, in a single variable, whose roots determine the co-ordinates of the scattering centres so as to obtain an infinitely resolved Patterson map [2].

[1] Cervellino A. and Ciccariello S. (1996). Rivista del Nuovo Cimento 19/8 1-59.

[2] Cervellino A. and Ciccariello S. (2001). J. of Phys. A 214, 739-750.